Question

ABCD is a square with side area 64 sq. cm. M and N are mid-points of sides AD and AB respectively. Find the area
of the shaded region.​

Answer 1

Area Of Shaded Region = 40 cm²

Step-by-step explanation:

GIVEN

Area Of Square = 64 square cm

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TO FIND

Area Of Shaded Region

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TRIANGLE MAN

We know that,

Area Of Square = Side × Side = Side²

64 = Side²

Side = √64

Side = 8

Side = 8 cm

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We know that,

M is the mid-point of AD

N is the mid-point of AB

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We know that,

Area Of Triangle = ½ × Base × Height

Here,

Base = AN = 8 / 2 = 4 cm

Height = AM = 8 / 2 = 4 cm

We know that,

Area Of Triangle = ½ × Base × Height

Area Of Triangle = ½ × 4 × 4

Area Of Triangle = ½ × 16

Area Of Triangle = 8

Area Of Triangle = 8 cm²

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TRIANGLE CBN

We know that,

Area Of Triangle = ½ × Base × Height

Here,

Base = BN = 8 / 2 = 4 cm

Height = BC = 8 cm

We know that,

Area Of Triangle = ½ × Base × Height

Area Of Triangle = ½ × 4 × 8

Area Of Triangle = ½ × 32

Area Of Triangle = 16

Area Of Triangle = 16 cm²

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We know that,

Area Of Shaded Region = Area Of Square ABCD - ( Area Of Triangle MAN + Area Of Triangle CBN )

Area Of Shaded Region = 64 - ( 8 + 16 )

Area Of Shaded Region = 64 - 24

Area Of Shaded Region = 40

Area Of Shaded Region = 40 cm²